52-x^2+2=10

Solution for 52-x^2+2=10 equation:

52-x^2+2=10

We move all terms to the left:

52-x^2+2-(10)=0

We add all the numbers together, and all the variables

-1x^2+44=0

a = -1; b = 0; c = +44;
Δ = b2-4ac
Δ = 02-4·(-1)·44
Δ = 176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*-1}=\frac{0-4\sqrt{11}}{-2}
=-\frac{4\sqrt{11}}{-2}
=-\frac{2\sqrt{11}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*-1}=\frac{0+4\sqrt{11}}{-2}
=\frac{4\sqrt{11}}{-2}
=\frac{2\sqrt{11}}{-1}
$